Boundary regularity and Hopf lemma for nondegenerate stable operators

Florian Grube

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arXiv · 2410.00829

Boundary regularity and Hopf lemma for nondegenerate stable operators

Florian Grube

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Abstract

We prove sharp boundary H{\"o}lder regularity for solutions to equations involving stable integro-differential operators in bounded open sets satisfying the exterior $C^{1,\text{dini}}$-property. This result is new even for the fractional Laplacian. A Hopf-type boundary lemma is proven, too. An additional feature of this work is that the regularity estimate is robust as $s\to 1-$ and we recover the classical results for second order equations.

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Florian Grube. 2024-10-01. Boundary regularity and Hopf lemma for nondegenerate stable operators. https://arxiv.org/abs/2410.00829

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